A flexible ranked set sampling schemes: Statistical analysis on scale parameter

A flexible ranked set sampling scheme including some various existing sampling methods is proposed. This scheme may be used to minimize the error of ranking and the cost of sampling. Based on the data obtained from this scheme, the maximum likelihood estimation as well as the Fisher information are studied for the scale family of distributions. The existence and uniqueness of the maximum likelihood estimator of the scale parameter of the exponential and normal distributions are investigated. Moreover, the optimal scheme is derived via simulation and numerical computations.